Easy -1.2 This is a routine linear programming/inequality graphing question requiring students to sketch three boundaries (two straight lines and a parabola) and shade the feasible region. It's a standard textbook exercise testing basic graphical skills with no problem-solving or novel insight required, making it easier than average.
Show in a sketch the region of the \(x\)-\(y\) plane within which all three of the following inequalities are satisfied.
$$3y \geqslant 4x \qquad y - x \leqslant 1 \qquad y \geqslant (x-1)^2$$
You should indicate the region for which the inequalities hold by labelling the region R. [4]
Correct identification of region (dependent on previous B marks); condone identification via shading so long as there is no ambiguity about the intended region
B1
Note that both lines and curve must meet at the same point for this final mark to be awarded (ignore labelling on axes)
$y = (x-1)^2$ drawn correctly | B1 | x-axis must be a tangent to the curve
$3y = 4x$ drawn correctly | B1 | Line must pass through the origin
$y - x = 1$ drawn correctly | B1 | Positive gradient and y-intercept
Correct identification of region (dependent on previous B marks); condone identification via shading so long as there is no ambiguity about the intended region | B1 | Note that both lines and curve must meet at the same point for this final mark to be awarded (ignore labelling on axes)
Show in a sketch the region of the $x$-$y$ plane within which all three of the following inequalities are satisfied.
$$3y \geqslant 4x \qquad y - x \leqslant 1 \qquad y \geqslant (x-1)^2$$
You should indicate the region for which the inequalities hold by labelling the region R. [4]
\hfill \mbox{\textit{OCR H240/03 2018 Q1 [4]}}